@rwallace8665DMG Poisons: If you crit with a poison coated weapon, do you double poison dice because crit, or not because saving throw? The intent is no. The saving throw, not the attack, determines whether the poison takes effect after a hit.
— Jeremy Crawford (@JeremyECrawford) November 24, 2014
what if they crit fail saving throw? then does it double?
There is no such thing as a “crit fail” in D&D, outside of attack rolls (which always miss when you roll a 1), and death saves (which count as 2 fails if you roll a 1).
Damage based on saves only does what it says it will, it doesn’t double unless specifically noted in the ability.